Evaluating Specification Tests for Markov‐Switching Time‐Series Models

Daniel R. Smith

29 citations0/0 files storedJournal of Time Series Analysis

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Financial Risk and Volatility Modeling Monetary Policy and Economic Impact Statistical and numerical algorithms

Abstract

Abstract. We evaluate the performance of several specification tests for Markov regime‐switching time‐series models. We consider the Lagrange multiplier (LM) and dynamic specification tests of Hamilton (1996) and Ljung–Box tests based on both the generalized residual and a standard‐normal residual constructed using the Rosenblatt transformation. The size and power of the tests are studied using Monte Carlo experiments. We find that the LM tests have the best size and power properties. The Ljung–Box tests exhibit slight size distortions, though tests based on the Rosenblatt transformation perform better than the generalized residual‐based tests. The tests exhibit impressive power to detect both autocorrelation and autoregressive conditional heteroscedasticity (ARCH). The tests are illustrated with a Markov‐switching generalized ARCH (GARCH) model fitted to the US dollar–British pound exchange rate, with the finding that both autocorrelation and GARCH effects are needed to adequately fit the data.

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References

1989A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle 1994Autoregressive conditional heteroskedasticity and changes in regime 2002International Asset Allocation With Regime Shifts 1996Modeling the conditional distribution of interest rates as a regime-switching process 2001Testing Density Forecasts, With Applications to Risk Management 1989A Markov Model of Heteroskedasticity, Risk, and Learning in the Stock Market 1994A Markov Model of Switching-Regime ARCH 1992The likelihood ratio test under nonstandard conditions: Testing the markov switching model of gnp

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